In this work, we present a theory that is able to explain the nonmonotonic decreasing behavior (observed in experimental data1-12) of the graphene terahertz conductivity with the increase of the field frequency. In this connection, the displacement of the structure of topological states inside the energy band gap, which appears in graphene due to the strong photon-electron coupling, and the narrowing of this gap, as result of electron transitions from bound photon-dressed electron states to extended states outside the energy gap driven by the field frequency, lead to a periodic change of singularities near the edge of the band gap, resulting in subtle quantum oscillations of the dynamical terahertz conductivity. This quantum contribution complements the Drude response, which fits the spectral range. On the other hand, the scattering processes by impurities favor interband transitions, suppressing this way intraband terahertz absorptions, which are related to optical transitions from inside to outside the gap.